Kirchhoff's rules

Kirchhoff’s rules, two statements about multi-loop electric circuits that embody the laws of conservation of electric charge and energy and that are used to determine the value of the electric current in each branch of the circuit.

The first rule, the junction theorem, states that the sum of the currents into a specific junction in the circuit equals the sum of the currents out of the same junction. Electric charge is conserved: it does not suddenly appear or disappear; it does not pile up at one point and thin out at another.

The second rule, the loop equation, states that around each loop in an electric circuit the sum of the emf’s (electromotive forces, or voltages, of energy sources such as batteries and generators) is equal to the sum of the potential drops, or voltages across each of the resistances, in the same loop. All the energy imparted by the energy sources to the charged particles that carry the current is just equivalent to that lost by the charge carriers in useful work and heat dissipation around each loop of the circuit.

On the basis of Kirchhoff’s two rules, a sufficient number of equations can be written involving each of the currents so that their values may be determined by an algebraic solution.

Kirchhoff’s rules are also applicable to complex alternating-current circuits and with modifications to complex magnetic circuits.

This article was most recently revised and updated by Erik Gregersen, Senior Editor.